Question

you know that the sum of -5 amd another integer is a positive integer. What can you conclude about the sign of the other integer? What can you conclude about the value of the other integer? Explain

Answer 1

We might directly answer the question by solving the inequality

$-5+x>0 \iff x>5$

So, the other number must be an integer greater than 5, and thus it must be positive.

From an intuitive point of view, we knew that the other number had to be positive. In fact, if you think of the numbers sitting on the number line, -5 sits five units to the left of 0. If we add a negative number, we go to the left, if we add a positive number, we go to the right. Since we want the result to be positive (i.e. to the right of 0), we have to go to the right, and so the unknown number must be positive.

Also, if we are 5 units to the left of 0, and we want to end to the right of 0, we must "walk" at least 6 steps, so that we fill the negative gap and end on the other side.